Calculus Single Variable, 10th Edition

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  • Edition: 10th
  • Format: Hardcover
  • Copyright: 2/28/2012
  • Publisher: Wiley

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The 10th edition of CalculusáSingle Variable continues to bring together the best of both new and traditional curricula in an effort to meet the needs of even more instructors teaching calculus. The author team's extensive experience teaching from both traditional and innovative books and their expertise in developing innovative problems put them in an unique position to make this new curriculum meaningful for those going into mathematics and those going into the sciences and engineering.á á This new text exhibits the same strengths from earlier editions including an emphasis on modeling and a flexible approach to technology.

Table of Contents

Before Calculusp. 1
Functionsp. 1
New Functions from Oldp. 15
Families of Functionsp. 27
Inverse Functionsp. 38
Limits And Continuityp. 49
Limits (An Intuitive Approach)p. 49
Computing Limitsp. 62
Limits at Infinity; End Behavior of a Functionp. 71
Limits (Discussed More Rigorously)p. 81
Continuityp. 90
Continuity of Trigonometric Functionsp. 101
The Derivativep. 110
Tangent Lines and Rates of Changep. 110
The Derivative Functionp. 122
Introduction to Techniques of Differentiationp. 134
The Product and Quotient Rulesp. 142
Derivatives of Trigonometric Functionsp. 148
The Chain Rulep. 153
Implicit Differentiationp. 161
Related Ratesp. 168
Local Linear Approximation; Differentialsp. 175
The Derivative In Graphing And Applicationsp. 187
Analysis of Functions I: Increase, Decrease, and Concavityp. 187
Analysis of Functions II: Relative Extrema; Graphing Polynomialsp. 197
Analysis of Functions III: Rational Functions, Cusps, and Vertical Tangentsp. 207
Absolute Maxima and Minimap. 216
Applied Maximum and Minimum Problemsp. 224
Rectilinear Motionp. 238
Newton's Methodp. 246
Rolle's Theorem; Mean-Value Theoremp. 252
Integrationp. 265
An Overview of the Area Problemp. 265
The Indefinite Integralp. 271
Integration by Substitutionp. 281
The Definition of Area as a Limit; Sigma Notationp. 287
The Definite Integralp. 300
The Fundamental Theorem of Calculusp. 309
Rectilinear Motion Revisited Using Integrationp. 322
Average Value of a Function and its Applicationsp. 332
Evaluating Definite Integrals by Substitutionp. 337
Applications Of The Definite Integral In Geometry, Science, And Engineeringp. 347
Area Between Two Curvesp. 347
Volumes by Slicing; Disks and Washersp. 355
Volumes by Cylindrical Shellsp. 365
Length of a Plane Curvep. 371
Area of a Surface of Revolutionp. 377
Workp. 382
Moments, Centers of Gravity, and Centroidsp. 391
Fluid Pressure and Forcep. 400
Exponential, Logarithmic, And Inverse Trigonometric Functionsp. 409
Exponential and Logarithmic Functionsp. 409
Derivatives and Integrals Involving Logarithmic Functionsp. 420
Derivatives of Inverse Functions; Derivatives and Integrals Involving Exponential Functionsp. 427
Graphs and Applications Involving Logarithmic and Exponential Functionsp. 434
L'H˘pital's Rule; Indeterminate Formsp. 441
Logarithmic and Other Functions Defined by Integralsp. 450
Derivatives and Integrals Involving Inverse Trigonometric Functionsp. 462
Hyperbolic Functions and Hanging Cablesp. 472
Principles Of Integral Evaluationp. 488
An Overview of Integration Methodsp. 488
Integration by Partsp. 491
Integrating Trigonometric Functionsp. 500
Trigonometric Substitutionsp. 508
Integrating Rational Functions by Partial Fractionsp. 514
Using Computer Algebra Systems and Tables of Integralsp. 523
Numerical Integration; Simpson's Rulep. 533
Improper Integralsp. 547
Mathematical Modeling With Differential Equationsp. 561
Modeling with Differential Equationsp. 561
Separation of Variablesp. 568
Slope Fields; Euler's Methodp. 579
First-Order Differential Equations and Applicationsp. 586
Infinite Seriesp. 596
Sequencesp. 596
Monotone Sequencesp. 607
Infinite Seriesp. 614
Convergence Testsp. 623
The Comparison, Ratio, and Root Testsp. 631
Alternating Series; Absolute and Conditional Convergencep. 638
Maclaurin and Taylor Polynomialsp. 648
Maclaurin and Taylor Series; Power Seriesp. 659
Convergence of Taylor Seriesp. 668
Differentiating and Integrating Power Series; Modeling with Taylor Seriesp. 678
Parametric And Polar Curves; Conic Sectionsp. 692
Parametric Equations; Tangent Lines and Arc Length for Parametric Curvesp. 692
Polar Coordinatesp. 705
Tangent Lines, Arc Length, and Area for Polar Curvesp. 719
Conic Sectionsp. 730
Rotation of Axes; Second-Degree Equationsp. 748
Indexp. I-1
Web Appendices (online only)
Available for download atwww.wiley.com/college/anton or atwww.howardanton.com and in WileyPLUS
Real Numbers, Intervals, And Inequalities
Absolute Value
Coordinate Planes, Lines, And Linear Functions
Distance, Circles, And Quadratic Equations
Early Parametric Equations Option
Mathematical Models
The Discriminant
Second-Order Linear Homogeneous Differential Equations
Web Projects: Expanding the Calculus Horizon (online only)
Available for download atwww.wiley.com/college/anton or atwww.howardanton.com and in WileyPLUS
Blammo The Human Cannonball
Comet Collision
Hurricane Modeling
Iteration And Dynamical Systems
Railroad Design
Table of Contents provided by Publisher. All Rights Reserved.

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